This paper presents a hybrid algorithm by applying a hybrid firefly and particle swarm optimization algorithm (HFPSO) to determine the optimal sizing of distributed generation (DG) and distribution static compensator (D-STATCOM) device. A multi-objective function is employed to enhance the voltage stability, voltage profile, and minimize the total power loss of the radial distribution system (RDS). Firstly, the voltage stability index (VSI) is applied to locate the optimal location of DG and D-STATCOM respectively. Secondly, to overcome the sup-optimal operation of existing algorithms, the HFPSO algorithm is utilized to determine the optimal size of both DG and D-STATCOM. Verification of the proposed algorithm has achieved on the standard IEEE 33-bus and Iraqi 65-bus radial distribution systems through simulation using MATLAB. Comprehensive simulation results of four different cases show that the proposed HFPSO demonstrates significant improvements over other existing algorithms in supporting voltage stability and loss reduction in distribution networks. Furthermore, comparisons have achieved to demonstrate the superiority of HFPSO algorithms over other techniques due to its ability to determine the global optimum solution by easy way and speed converge feature.
A hybrid algorithm for voltage stability enhancement of distribution systems
1. International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 1, February 2022, pp. 50~61
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i1.pp50-61 ο² 50
Journal homepage: http://ijece.iaescore.com
A hybrid algorithm for voltage stability enhancement of
distribution systems
Hazim Sadeq Mohsin Al-Wazni, Shatha Suhbat Abdulla Al-Kubragyi
Department of Electrical Engineering, Technology University, Baghdad, Iraq
Article Info ABSTRACT
Article history:
Received Feb 26, 2021
Revised Jun 18, 2021
Accepted Jun 29, 2021
This paper presents a hybrid algorithm by applying a hybrid firefly and
particle swarm optimization algorithm (HFPSO) to determine the optimal
sizing of distributed generation (DG) and distribution static compensator
(D-STATCOM) device. A multi-objective function is employed to enhance
the voltage stability, voltage profile, and minimize the total power loss of the
radial distribution system (RDS). Firstly, the voltage stability index (VSI) is
applied to locate the optimal location of DG and D-STATCOM respectively.
Secondly, to overcome the sup-optimal operation of existing algorithms, the
HFPSO algorithm is utilized to determine the optimal size of both DG and
D-STATCOM. Verification of the proposed algorithm has achieved on the
standard IEEE 33-bus and Iraqi 65-bus radial distribution systems through
simulation using MATLAB. Comprehensive simulation results of four
different cases show that the proposed HFPSO demonstrates significant
improvements over other existing algorithms in supporting voltage stability
and loss reduction in distribution networks. Furthermore, comparisons have
achieved to demonstrate the superiority of HFPSO algorithms over other
techniques due to its ability to determine the global optimum solution by
easy way and speed converge feature.
Keywords:
D-STATCOM
HFPSO algorithm
Smart distribution grid
Voltage stability
This is an open access article under the CC BY-SA license.
Corresponding Author:
Hazim Sadeq Mohsin Al-Wazni
Department of Electrical Engineering, Technology University
Industrial Street, Baghdad, Iraq
Email: hazimwazni83@gmail.com
NOMENCLATURE
ππ : The voltage at receiving end bus π₯π(π‘) : Size of particles
ππ : The voltage at sending end bus π₯π(π‘ + 1) : Updated size of the particles
ππ πππ€ : The voltage at receiving end bus after
compensated
ππ(π‘)
π£π(π‘ + 1)
: Velocities of the particles
: Updated velocities of the particles
ππππ€ : Phase angle between ππ πππ€ and ππ π‘ : Number of iteration
πΏ : Phase angle of sending end voltage πΌπ·βπππ΄ππΆππ : The injected current of D-STATCOM
πΌ : Phase angle of Current pass between
two buses
ππ‘ππ‘ππ πππ π
π ππ + ππππ
: Total power losses
: Impedance of branch between bus 'S' and 'R'
ππ ,πππ : Minimum Voltage limit of bus 'R' π½2 and π½3 : Weighting factors of objective functions Ξ²_1
ππ ,πππ₯ : Maximum Voltage limit of bus 'R' ππ·πππ΄ππΆππ(π ) : Reactive power of D-STATCOM at bus βRβ
ππ (π )
πππΌπ
: Real power of DG at bus βRβ
: Voltage stability index of node 'R'
πππΏ : Total real loss before insert DG and D-
STATCOM
π΄π(π₯)
π
: Average of buses voltages
: Weight inertia
βπππΏ
π·πΊ π·ππ
β : Loss Reduction Index with DG and D-
STATCOM
π2,π1
πΌπΏ
: Acceleration coefficients
: Current pass between two buses
ππ·πππ΄ππΆππ(π )
πππ
, ππ·πππ΄ππΆππ(π )
πππ₯ : Minimum, maximum injected reactive power
limit of compensated bus' R'
ππππ π‘π‘β1 : Global best size ππ ,min(π ), ππ ,max(π ) : Maximum, minimum real power limit of
compensated bus 'R'
2. Int J Elec & Comp Eng ISSN: 2088-8708 ο²
A hybrid algorithm for voltage stability enhancement of β¦ (Hazim Sadeq Mohsin Al-Wazni)
51
ππππ π‘π : Particle best size ππππ π (π, π ), ππππ π (π, π ) : Real and reactive power losses of branch
between bus 'S' and 'R'
1. INTRODUCTION
Nowadays, transmission and distribution power systems are facing a challenge to provide the power
demands for more customers with better quality and higher reliability at a lower cost. Such growing demand
increasing power transfer through lines which is limited by the thermal, voltage, and stability of lines.
Consequently, when the lines are operated near to their critical limits of power angles or voltage limits, any
increased demand in this system would results instability like power system oscillation and voltage collapse
occurrence which may lead to generator outages and ultimately blackout [1].
Different techniques have been suggested by researchers for solving the voltage system stability
issues and minimizing losses in distribution systems. Previosly, system planners are inclined to develop new
lines. However, such technique is difficult to implement due to some of the economic and environmental
concerns [2], [3]. So, these various restrictions on the construction of new transmission lines have persuaded
the power system designers to look for some alternative solutions,so to increase the power system stability
and efficiently transmit power over the transmission lines [4].
To minimize the probability of voltage collapse happening and enhance voltage stability as well as
improve voltage profile, some researchers have proposed to add capacitors in an optimal location with
optimal size by using different optimization techniques such as harmonic search (HS) algorithm [5], dice
game optimization (DGO) [6], and modified biogeography based optimization (MBBO) algorithm [7].
However, these shunt capacitors are not capable to constantly produce a variable reactive power and exhibit
some of the operational problems like resonance [2]. Such restrictions of the construction of shunt capacitors
have persuaded the power system designers to look for some alternative solutions.
Recently, distribution generators (DG) are widely known as "an electric power source connected
directly to the distribution network or on the customer side of the meter'', that form the key part of the
solutions [8]. DGs are known as small distributed generators which are consisted of renewable and
nonrenewable power sources. DGs are contributed to the centralized power grids that are managed at the
distribution level [9]. The integration of renewable energy sources in the conventional distribution system is
becoming valuable and more attractive due to their economic and technical impacts [10]. Many researcher
have adopted various types of renewable sources (fuel cell, PV, battery, biomass, wind) [11]-[14]. However,
advanced devices are required to control and manage the new smart distribution grids to operate with
bidirectional power flow using power electronics and energy storage units [15]. Combining the use of the
distributed flexible ac-transmission system (D-FACTS) as a power electronic device with DG in the
distribution networks will mitigate the problems of environmental, reliability, and stability issues [2].
The distributed static synchronous compensator (D-STATCOM) is the most important type of
shunt-connected D-FACTS device, it is connected directly to low voltage distribution grids without any
ancillary components which represents as an efficient shunt capacitors substitute [2]. It acts as a reactive
power compensation source, harmonics reduction, power factor correction, and controlling the voltage of the
distribution network [16]. Recently, the combination of DG and D-STATCOM was suggested which could
compensate for the active and reactive power in smart distribution grids. The optimal location and the
capacity of DGs of these sources are some of the main factors of contribution in affecting the improvement of
the power quality indices such as the reduction of the distribution systems losses and maintaining the voltage
profile within acceptable limits [17].
A DG with D-STATCOM was tested under different conditions to enhance the voltage stability of
different load models [2], [18]. Several studies have been presented under the name of metaheuristic
techniques such as βwhale optimization algorithm (WOA) [17], noval light search algorithm (LSA) [2],
gravitational search algorithm (GSA) [19], a combination of genetic algorithm and particle swarm
optimization (GA and PSO) [20], grey wolf optimization algorithm (GWOA) [21], vortex searching
algorithm [22], imperialist competitive algorithm (ICA) [8], and hybrid genetic and ant colony algorithm
[16]β to determine the optimal placement problem of DG and D-STATCOM in smart power systems. Many
of the above studies mentioned above have been carried out to locate the optimal location and size problems
of DG and D-STATCOM devices separately or simultaneously.
Remarkably, a comprehensive study is lacking in using intelligent algorithms in exploiting the
potentials of the DGs with D-STATCOM. Although, several studies have presented under the name of
metaheuristic techniques. PSO and general algebraic modeling systems were proposed to solve the sizing and
location of single and multiple D-STATCOM in [23]. An artificial fish swarm optimization algorithm
(AFSOA) using voltage stability index (VSI) and loss sensitivity factor (LSF) was applied to deduce the size
and optimal locations of DGs and D-STATCOM in [24].
3. ο² ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 50-61
52
Further, research on using the VSI and WOA was developed to select the proper location and best
size of DG, so to enhance the voltage stability and increase the load-ability through injecting the appropriate
active and reactive powers. However, the best DG place is allocating by using the VSI to find the most
sensitive buses [25]. The literature clarified that the researchers are continuing to develop intelligent
optimization techniques to solve global optimization problems. This paper has proposed to exploit the
advantage of firefly algorithm (FA) and PSO as a fast converge optimization algorithm with good-tuning
feature, so to easily achieve the global optimum solution for optimal placement and sizing of DG and D-
STATCOM device to support the gridβs voltage stability as well as enhance voltage profile and minimize
power losses.
The motivation of this study focuses on the tabulated results which illustrate the ability of the hybrid
firefly and particle swarm optimization algorithm (HFPSO) to determine the optimal placement and sizing of
DG and D-STATCOM device, due to its feature to find the global optimum solution. The algorithm is based
on a multi-objective HFPSO to minimize the system power losses and voltage profile enhancement as well as
increasing the system stability. The verification of the proposed algorithm is achieved on the standard IEEE
33-bus and Iraqi 65-bus radial distribution systems through simulation using MATLAB.
This paper is organized as follows. Section 2 explains the system modeling, While section 3
presents the problem formulation. A hybrid algorithm combining the firefly algorithm and particle swarm
optimization is introduced in section 4. In section 5, the simulation results of a distribution system under
different cases with the proposed algorithm are presented. Furthermore, a performance comparison of the
system is then carried out against other existing algorithms in supporting voltage stability and loss reduction
in the distribution networks. Finally, section 6 gives concluding remarks on the current work.
2. SYSTEM MODELLING
2.1. D-STATCOM modelling
D-STATCOM is well-known as an efficient power electronic device control power flow [16], [26].
The basic function of the D-STATCOM is providing reactive power that depends on the reactive power
exchange between the AC grid and the D-STATCOM with fast and uninterrupted power [16], [21], [27]. The
injected reactive power deduce by (1).
ππ·βπππ΄ππΆππ = π
ππππ€ (πΌπ·βπππ΄ππΆππ)β
(1)
Where πΌπ·βπππ΄ππΆππβ ((
π
2
) + ππππ€) is the injected current by DSTATCOM ππ πππ€ = ππ πππ€β ππππ€ is the
voltage of bus βRβ after correction. Figure 1(a) shows the single line diagram of two buses of a distribution
system with D-STATCOM that is installed in bus βRβ Voltage of bus βRβ changes from ππ to ππ πππ€ as shown
in Figure 1(b).
(a) (b)
Figure 1. Single line diagram and the phasor diagram of two buses with D-STATCOM: (a) single line
diagram of two buses with D-STATCOM [21], (b) the phasor diagram of two buses with D-STATCOM [21]
ππ πππ€β ππππ€ = ππβ πΏ β (π ππ + ππππ )πΌπΏβ πΌ β (π ππ + ππππ )πΌπ·βπππ΄ππΆππβ ((
π
2
) + ππππ€) (2)
4. Int J Elec & Comp Eng ISSN: 2088-8708 ο²
A hybrid algorithm for voltage stability enhancement of β¦ (Hazim Sadeq Mohsin Al-Wazni)
53
DSTATCOM is one of the most efficient D-FACTS devices due to its features like zero resonance,
less harmonic distortion, low power losses, low cost, compact size and high regulatory capability [16], [28].
D-STATCOM has been employed as multi-applications at the distribution grids, so to enhance voltage
profile, minimize real power loss, improves load ability, and enhances stability [21]. However, the proper
location of D-STATCOM is important to minimize the network power loss and subject to the following
standard limits [29]:
ππππ‘πππ πππππ‘: ππ ,πππ β€ ππ β€ ππ ,πππ₯
where ππ ,πππ is the minimum voltage limits of bus 'R' and ππ ,πππ₯ is the maximum voltage limits of bus 'R'.
πΌπππππ‘ππ πππππ‘ππ£π πππ€ππ πππππ‘: ππ·πππ΄ππΆππ(π)
πππ
β€ ππ·πππ΄ππΆππ(π) β€ ππ·πππ΄ππΆππ(π)
πππ₯
π = 1,2,3 , ππ
Where ππ·πππ΄ππΆππ(π )
πππ
is the minimum reactive power limit of the compensated bus 'R' and ππ·πππ΄ππΆππ(π )
πππ₯
is
the maximum reactive power limit of the compensated bus 'R'.
2.2. Distributed generation (DG)
DG is described as a small-scale electric power generation that has a capacity of 1 kW to 100 MW
and linked adjacent to the loads. DG consists of renewable and nonrenewable sources such as micro turbines,
induction generators, synchronous generators, solar photovoltaic, fuel cells, combustion gas turbines, wind
turbines, and other small power generation sources. DG sources are classified into the following four types
[22]:
a) DG type one: DG injects real power (P) only
b) DG type two: DG injects both real and reactive power (P and Q)
c) DG type three: DG injects real (P) power but absorbs reactive power (Q)
d) DG type four: DG injects reactive power (Q) only
The main features of DGs are mitigating the greenhouse effect and using fossil fuel, improve
voltage profile, energy security, reliability, stability, power quality, and reduces power losses [8], [9], [29].
Nevertheless, the optimal locations of DGs are also important to improve the system operation characteristics
and subject to the following standard limits [30]:
ππππ‘πππ πππππ‘: ππ ,πππ β€ ππ β€ ππ ,πππ₯
πΌπππππ‘ππ πππππ‘ππ£π πππ€ππ πππππ‘: ππ ,min(π) β€ ππ (π) β€ ππ ,max(π) π = 1,2,3 , ππ
where ππ ,min(π ) is the minimum real power limit of the compensated bus 'R' and ππ ,max(π ) is the maximum
real power limit of the compensated bus 'R'.
3. PROBLEM FORMULATION
3.1. Load flow analysis
The direct load flow analysis is considered in this paper to find the power losses and voltage profiles
of each bus developed for the radial distribution systems. The power-flow equations are written according to
Kirchhoff's Current Law, a more detailed explanation of the power flow analysis can be found in [27]. The
sample distribution system is shown in Figure 2. The voltage at bus 'R' is written as in (3):
ππ = π
π β π΅π β (π π π + πππ π ) (3)
where π΅π is the bus-currents to branch-currents matrix. The total power loss of the network is calculated by
summing the power losses of all the branch as shown in (4) [2]:
ππ‘ππ‘ππ πππ π = β ππππ π (π, π )
ππ.πππππβ
π =1
+ π β ππππ π (π, π )
ππ.πππππβ
π =1
(4)
where the power loss in a branch between buses 'S 'and 'R' is identified by using (5) and (6) for real and
reactive losses respectively.
5. ο² ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 50-61
54
ππππ π (π, π ) = (
ππ
2
+ ππ
2
|π
π |2
) β π π π (5)
ππππ π (π, π ) = (
ππ
2
+ ππ
2
|π
π |2
) β ππ π (6)
Figure 2. Single line diagram of two buses system [21]
3.2. Objective function
The multi-objective function should be modeled carefully to avoid conflicting between various
single objective functions. In this paper, the objective function of the proposed algorithm is adopt a number
of functions to be optimized simultaneously such as maximize voltage stability index, mitigate the power loss
and enhance the bus voltage profile with a weighting factor. The weight factors are considered to determine
the priority impact of every single objective function for DG/D-STATCOM interconnection. Due to the fact
that, power losses have a greater effect on utilities and represent the major concern in the power system
network. Therefore, it should be reduced by selected appropriate weight factors more imperative than the
influence voltage stability index and voltage profile. Mathematically, the multi-objective function has as
shown in (7):
πππππππ§π(πΉππ‘π‘πππ π ) = πππ (π½1(βπππΏ
π·πΊ π·ππ
β
) + π½2 (
1
π΄π(π₯)
) + π½3 (
1
β πππΌπ·πΊ π·ππ
β
)) (7)
where βπππΏ
π·πΊ π·ππ
β
is the ratio of the total power loss after and before adding DG/D-STATCOM in radial
distribution system (RDS) which given by (8) [17].
βπππΏ
π·πΊ π·ππ
β
=
πππΏ
π·πΊ π·ππ
β
πππΏ (8)
β πππΌπ·πΊ π·ππ
β
is the ratio of the voltage stability index of weaken bus after and before adding
DG/D-STATCOM in RDS which is given by (9) [2].
β πππΌπ·πΊ π·ππ
β
=
πππΌπππ‘ππ
π·πΊ π·ππ
β
πππΌπππππ (9)
π΄π(π₯) is the average of buses voltages which is given by (10) [15].
π΄π(π₯) = (
β ππ(π₯)
π
π=1
π
) (10)
π½1, π½2 and π½3 are the weighting factors of the minimization power loss and maximization AV and VSI
respectively which are considered as (0.7), (0.3), and (0.3) respectively.
3.3. Voltage stability index
Voltage stability is the ability of a power system to meet the increasing demand and maintain the
voltage at all buses in an acceptable limit and to avoid the occurrence of the voltage collapse. The voltage
6. Int J Elec & Comp Eng ISSN: 2088-8708 ο²
A hybrid algorithm for voltage stability enhancement of β¦ (Hazim Sadeq Mohsin Al-Wazni)
55
collapse is defined as a very low voltage profile in a significant number of the system buses with a sequence
of events accompanying voltage instability [1], [31].
The power system security level can be reflected by many possible indices. In this part, the VSI is
applied pre-identify to identify the weak buses of radial distribution networks, in order to strengthen these
buses and maintain system voltages at an acceptable level. It will add DGs and D-STATCOM in an optimal
location. Then, to overcome the sup-optimal operation of the existing algorithms, the HFPSO algorithm is
utilized to determine the optimal size of both DG and D-STATCOM. Moreover, the predetermining
advantage of the optimal location by using VSI to minimize the search space of the optimization algorithm.
The monetary value of voltage stability index can be formulated as relation in (11) [22], [24]:
πππΌπ =β£ ππ β£4
β 4(ππ πππ β ππ π π π )2
ββ£ π
π β£4 (ππ π π π + ππ ππ π ) (11)
where πππΌπ is the voltage stability index of node 'R' for the distribution system, which is shown in Figure 3.
4. HYBRID FIREFLY AND PARTICAL SWARM OPTIMIZATION (HFPSO)
A HFPSO is used in this study so to find the optimum DG and D-STATCOM placement and sizing.
The HFPSO is introduced firstly by [32] to solve the optimization problem. The performance of the proposed
hybrid optimization algorithm has significant improvements over the standard PSO and FA algorithms due to
the combination of the advantages and strengths of PSO and FA, and also because it mitigates the
disadvantages of these algorithms. Generally, it provides a fast convergence as PSO feature and easily
achieves the global optimum solution as a good-tuning feature of FA [32]. Figure 3 shows the flowchart of
the proposed hybrid of FA and PSO.
Figure 3. Flowchart of HFPSO algorithm [32]
7. ο² ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 50-61
56
To illustrate the HFPSO algorithm, the steps of the algorithm steps are described below:
1. Input the parameters that are used by both algorithms and initialize particles with random positions and
velocities. In the considered case, the location of D-STATCOM and DG are generated in a form of
vectors as algorithm particles.
2. Run the load flow program to calculate the fitness of each particle according to (7).
3. Calculate the global and personal best particles and then assigned
4. An improvement is done in its fitness value in the last iteration according to (12).
π(π, π‘) = {
π‘ππ’π, ππ πππ‘πππ π (ππππ‘πππππ
π‘
) β€ ππππ π‘π‘β1
ππππ π. ππ πππ‘πππ π (ππππ‘πππππ
π‘
) > ππππ π‘π‘β1 (12)
5. Save the current position in a temp variable (π₯πβπ‘πππ) and calculate the new position and velocity
according to (13) and (14).
π₯π(π‘ + 1) = π₯π(π‘) + π΅Β°πβπΎπ2ππ
(π₯π(π‘) β ππππ π‘π‘β1
) + α΅βπ (13)
π£π(π‘ + 1) = π₯π(π‘ + 1) β π₯πβπ‘πππ (14)
6. Start the local search and handle particle by an imitative FA if a particle has a better or equal fitness value
than the previous global best, otherwise, PSO continues its standard processes with a particle according to
(15) and (16) so to handle this particle.
ππ(π‘ + 1) = π€ππ(π‘) + π1π‘1(ππππ π‘π(π‘) β π₯π(π‘)) + π2π‘2(ππππ π‘π(t) β π₯π(t)) (15)
π₯π(π‘ + 1) = π₯π(π‘) + ππ(π‘ + 1) (16)
7. Run the load flow to calculate the fitness of each particle, select the dominant one and consider it as best
global fitness if it was better than the previous global fitness.
8. Update the best position of each particle by comparing the new position to the best global position.
9. If the algorithm converges, the optimization process is over. Print the optimal solution, or otherwise, go to
step 4.
5. RESULTS AND DISCUSSION
To demonstrate the performance of the HFPSO method, a standard IEEE 33-bus RDS and 65-bus
Iraqi RDS are used and simulated using the MATLAB. The losses and bus voltage for all the systems are
calculated through the direct load flow analysis. The optimal location and sizing of DG and D-STATCOM
are obtained by the proposed optimization algorithm HFPSO. To demonstrate the effectiveness of the
proposed algorithm, the overall findings/results are compared with other optimization techniques such as;
bacterial foraging optimization algorithm (BFOA) [18] and the PSO [10], [33], [34] for four different cases
as follows: i) case 1 the system without DG and D-STATCOM, ii) case 2 the system with only D-
STATCOM, iii) case 3 the system with only DG and iv) case 4 the system with multi DG and D-STATCOM.
5.1. 33-bus test system
A bus test radial distribution system is considered in this paper. To show the effectiveness of the
proposed method, four different case studies have been tested. The data of the system are taken from [35].
The total load of the system is 3715 kW and 2300 KVar with the base apparent power and base voltage are
100 MVA and 12.66 kV respectively. The comparative simulation results of the proposed algorithm and
other optimization techniques are shown in Table 1. Firstly, the system without DG and D-STATCOM as a
base case is simulated. So, the active power losses, the minimum VSI, and the minimum voltage are
210.77 kW, 0.66734 p.u, and 0.90383 p.u, respectively as indicated in Table 1.
Then, the D-STATCOM is placed at 30th
bus as the optimal location (case 2), the total power loss
has been reduced to 143.6 kW and the minimum VSI is enhanced to 0.7355 p.u, while the results obtained in
[18] are 144.38 kW and 0.7228 p.u respectively. In this case, the authors have taken the line data of RDS
presented in [36], [37] which differs from the line data considered in this paper but the same line data
considered in [27] in case placement D-STATCOM. In case 3, one DG (type one) is optimally placed in the
6th
, bus with 2720 kW as an optimal size. The total power loss is reduced to 111.23 kW and the minimum
8. Int J Elec & Comp Eng ISSN: 2088-8708 ο²
A hybrid algorithm for voltage stability enhancement of β¦ (Hazim Sadeq Mohsin Al-Wazni)
57
VSI of this system is enhanced to 0.7949 p.u. Clearly, the power loss reduction and VSI enhancement, in this
case, are better than other optimization methods as illustrates in Table 1. Finally, in case 4, three DG and
three D-STATCOM are placed in the system at optimal locations to reduce the power losses and to improve
the minimum VSI of this system. The obtained results are presented in Table 1. The total power loss is
reduced to 13.8 kW and the minimum VSI is enhanced to 0.9415 p.u. It is noticed that the results in case 4
are better than the results of other algorithms. Obviously, the HFPSO gives a good reduction in losses and the
voltage profile of the system has been improved noticeably compared to other algorithms. A comparison of
the voltage profile, stability voltage index and the total power losses for the four different cases are shown in
Figure 4(a), 4(b), and 4(c) respectively.
Table 1. The comparative simulation results
Variable HFPSO BFOA [18] PSO [10], [33], [34]
Case 1 Ploss (kW) 210.77 210.98 210.99
VSImin (p.u.) 0.66734 0.6610 0.6671
Vmin (p.u.) 0.90383 0.9037 0.9038
Case 2 Size in kVAr (location) 1300 (30) 1102.7 (30) 1233 (7)
Ploss (kW) 143.6 144.38 153
VSImin (p.u.) 0.7355 0.7228 0.726
Vmin (p.u.) 0.9261 0.922
Case 3 Size in kW (location) 2720(6) 2200 (6) 2895.1 (7)
Ploss (kW) 111.23 113.14 114.89
VSImin (p.u.) 0.7949 0.7640
Vmin (p.u.) 0.9442 0.9368 0.9501
Case 4 Size in kVAr (location) 390 (12)
650 (24)
840 (30)
400 (12)
350 (25)
850 (30)
603.4 (8)
466.3 (22)
856.7 (30)
Size in kW (location) 880 (12)
870 (24)
1030 (30)
850 (12)
750 (25)
860 (30)
1015.4 (9)
351.4 (24)
8445 (30)
Ploss (kW) 13.8 15.07 27.3993
VSImin (p.u.) 0.9415 0.9376
Vmin (p.u.) 0.985 0.9862 0.975
(a) (b)
(c)
Figure 4. Comparison of results for the four different cases: (a) comparison of voltage profiles for different
cases in 33-bus system, (b) comparison of VSI for different cases in 33-bus system, and (c) comparison of
line losses for different cases in 33-bus system
9. ο² ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 50-61
58
5.2. The 65-bus system numerical results
The Iraqi real 65-bus radial distribution system is simulated as a second test system under four
different case studies. Figure 5 shows the systemβs configuration. The system data is given in Table 2 and the
results are presented in Table 3. The total load of this RDS is 5669.1 kW and 3560.6 KVar with base
apparent power and base voltage are 100 MVA and 11 kV respectively. The active power losses, the
minimum VSI, and the minimum voltage of the base case are 446.2 kW, 0.645 p.u, and 0.8962 p.u,
respectively.
Figure 5. Iraqi real 65-bus configuration
Table 2. 65 bus system data
From To R (p.u) ππΏ ππΏ To R (p.u) X (p.u) ππΏ (MW) ππΏ (MVAr)
1 1 2 0.216363 (MW) (MVAr) 33 34 0.006175 0.007538 0.1700 0.1054
2 2 3 0.18478 0.1063 0.0659 34 35 0.045125 0.055081 0.1063 0.0659
3 3 4 0.159363 0.1063 0.0659 35 36 0.032063 0.039137 0.1063 0.0659
4 4 5 0.06318 0.0 0.000 36 37 0.030875 0.037687 0.0 0.000
5 4 6 0.025650 0.1700 0.1054 37 38 0.046550 0.056820 0.1063 0.0659
6 6 7 0.011400 0 0 38 39 0.015200 0.018554 0.0 0.0
7 6 8 0.077663 0.1063 0.0659 39 40 0.056763 0.069286 0.1700 0.1054
8 8 9 0.004750 0.0 0.00 40 41 0.018763 0.022902 0.0 0.0
9 8 10 0.073625 0.1063 0.0659 41 42 0.021138 0.025801 0.1063 0.0659
10 10 11 0.022325 0.0 0.000 42 43 0.045600 0.055661 0.1700 0.1054
11 10 12 0.024938 0.1063 0.0659 43 44 0.022088 0.026961 0.1063 0.0659
12 12 13 0.066025 0.0 0.000 44 45 0.026363 0.032179 0.1700 0.1054
13 12 14 0.032300 0.1700 0.1054 45 46 0.037525 0.045804 0.0 0.00
14 14 15 0.030875 0.1700 0.1054 46 47 0.055813 0.068127 0.1063 0.0659
15 15 16 0.031588 0.0 0.0 47 48 0.007600 0.009277 0.1063 0.0659
16 15 17 0.089538 0.1700 0.1054 48 49 0.021375 0.026091 0.0 0.000
17 17 18 0.017100 0.0 0.0 49 50 0.009975 0.012176 0.1063 0.0659
18 17 19 0.014725 0.1063 0.0659 50 51 0.029688 0.036238 0.1700 0.1054
19 19 20 0.015675 0.0 0.000 51 52 0.006413 0.007827 0.0 0.000
20 19 21 0.095238 0.1063 0.0659 52 53 0.081225 0.099146 0.1700 0.1054
21 21 22 0.121838 0.0 0.0 53 54 0.016150 0.019713 0.0 0.000
22 21 23 0.113050 0.1700 0.1054 54 55 0.018525 0.022612 0.1700 0.1054
23 23 24 0.016388 0.0 0.0 55 56 0.018763 0.022902 0.1700 0.1054
24 23 25 0.011400 0.1700 0.1054 56 57 0.002850 0.003479 0.1063 0.0659
25 25 26 0.001663 0.0 0.0 57 58 0.013538 0.016524 0.1063 0.0659
26 25 27 0.027550 0.1063 0.0659 58 59 0.012588 0.015365 0.0 0.00
27 27 28 0.008550 0.0 0.0 59 60 0.009500 0.011596 0.1063 0.0659
28 28 29 0.011638 0.1063 0.0659 60 61 0.050113 0.061169 0.1700 0.1054
29 29 30 0.020900 0.1700 0.1054 61 62 0.026125 0.031889 0.1063 0.0659
30 27 31 0.015675 0.1700 0.1054 62 63 0.022800 0.027830 0.0 0.000
31 31 32 0.021613 0.0 0.0 63 64 0.021138 0.025801 0.1700 0.1054
32 31 33 0.069113 0.1700 0.1054 64 65 0.024938 0.030439 0.1700 0.1054
It is depicted from Table 3 the total power loss is reduced to 300.3 kW and the minimum VSI is
enhanced to 0.7941 p.u after D-STATCOM is placed at the 33th
bus as the optimal location in case 2. While
10. Int J Elec & Comp Eng ISSN: 2088-8708 ο²
A hybrid algorithm for voltage stability enhancement of β¦ (Hazim Sadeq Mohsin Al-Wazni)
59
in case 3, one DG (type one) is optimally placed in the 33th
bus with 5020 kW as the optimal size. The total
power loss is reduced to 122 kW and the minimum VSI of this system is enhanced to 0.8367 p.u. In case 4,
both three DG and one D-STATCOM are installed at optimal locations to reduce the power losses and to
improve the minimum VSI of this system. The obtained results are presented in Table 3. However, the total
power loss is reduced to 12.2 kW and the minimum VSI is enhanced to 0.9707 p.u after a multi DG and D-
STATCOM are placed at the optimal locations. A comparison of the voltage profile, stability voltage index,
and the total power losses for the four different cases are shown in Figure 6(a), 6(b), and 6(c) respectively.
Table 3. 65-bus numerical results
Case 1 Case 2 Case 3 Case 4
Size in MVAr (location) 3.34 (33) 2.77 (33)
Size in MW (location) 5.02 (33) 3.96 (34)
0.39 (39)
1.62 (3)
Ploss (kw) 446.2 300.3 122 12.2
Qloss (kvar) 544.6 367 148.9 14.9
VSImin (p.u.) 0.645 0.7941 0.8367 0.9707
Vmin (p.u.) 0.8962 0.9440 0.9564 0.9926
(a) (b)
(c)
Figure 6. Comparison of results losses for the four different cases: (a) comparison of voltage profiles for
different cases in Iraqi 65-bus system, (b) comparison of VSI for different cases in Iraqi 65-bus system, and
(c) comparison of line losses for different cases in Iraqi 65-bus system
6. CONCLUSION
In this paper, a new optimization technique based on HFPSO has been proposed to enhance the
system stability of smart distribution grids. The main advantage of the proposed algorithm is to combine the
advantages and strengths of PSO and FA and to mitigate the disadvantages of these algorithms. HFPSO is
employed to solve a multi-objective function including voltage stability enhancement and minimizing the
11. ο² ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 50-61
60
total power loss by finding the optimal locations and sizes of DG and D-STATCOM in the power distribution
system. Actually, The effectiveness of the proposed algorithm has been tested on two power systems.
Besides, the overall results were, compared with some other optimization techniques such as BFOA and PSO
under four different cases. Comprehensive simulation results show that the proposed HFPSO algorithm
achieves significant improvements compared to other optimization algorithms in supporting voltage stability
and in minimizing the power losses in distribution networks. Generally, HFPSO provides a fast convergence
as PSO feature and easily achieves the global optimum solution as a good-tuning feature of the firefly
algorithm. Furthermore, it could be concluded that the HFPSO would simplify the use, as an intelligent real-
time tool with any large distribution system.
REFERENCES
[1] N. Ghaffarzadeh, H. Marefatjo, and I. Soltani, βInvestigation and comparison of the effect of facts devices, capacitors and lines
reactance variations on voltage stability improvement and loadability enhancement in two area power system,β International
Journal of Applied Power Engineering (IJAPE), vol. 1, no. 3, pp. 145-158, 2012, doi: 10.11591/ijape.v1i3.1618.
[2] Y. Thangaraj and R. Kuppan, βMulti-objective simultaneous placement of DG and DSTATCOM using novel lightning search
algorithm,β Journal of Applied Research and Technology, vol. 15, no. 5, pp. 477-491, 2017, doi: 10.1016/j.jart.2017.05.008.
[3] R. H. Al-Rubayi and S. S. A. Alhalim, βStability improvement of the (400 kV) Iraqi grid using the best FACTS devices,β
Engineering and Technology Journal, vol. 33, no. 7, pp. 1598β1618, 2015.
[4] Q. W. Ali and A. Ul Asar, βSmart power transmission system using FACTS device,β International Journal of Applied Power
Engineering (IJAPE), vol. 2, no. 2, pp. 61-70, 2013, doi: 10.11591/ijape.v2i2.1606.
[5] M. Suneetha, R. Srinivasa Rao, and B. Subramanyam, βImplement the harmonic search algorithm with optimum location of
capacitors sizing and dispatchable DGs to control the reactive power on interconnected bus system,β Journal of Advanced
Research in Dynamical and Control Systems, vol. 11, no. 1, pp. 880-889, 2019, doi: 10.11591/ijra.v7i3.pp149-158.
[6] M. Dehghani, Z. Montazeri, O. P. Malik, K. Al-Haddad, J. M. Guerrero, and G. Dhiman, βA new methodology called dice game
optimizer for capacitor placement in distribution systems,β Electrical Engineering amd Electromechanics, vol. 2020, no. 1,
pp. 61-64, 2020, doi: 10.20998/2074-272x.2020.1.10.
[7] H. F. Kadom, A. N. Hussain, and W. K. S. Al-Jubori, βDual technique of reconfiguration and capacitor placement for distribution
system,β International Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 1, pp. 80-90, 2020,
doi: 10.11591/ijece.v10i1.pp80-90.
[8] N. Ghaffarzadeh, M. Akbari and A. Khanjanzadeh, βDistributed generation allocation to improve steady state voltage stability of
distribution networks using imperialist competitive algorithm,β International Journal of Applied Power Engineering (IJAPE),
vol. 2, no. 2, pp. 71-78, 2013, doi: 10.11591/ijape.v2.i2.pp71-78.
[9] A. H. Kadam, K. Unni, and S. Thale, βPerformance analysis of voltage stability against sudden load changes in voltage controlled
inverters for distributed generation,β International Journal of Applied Power Engineering (IJAPE), vol. 3, no. 1, pp. 33-40, 2014,
doi: 10.11591/ijape.v3.i1.pp33-40.
[10] A. Lasmari, M. Zellagui, R. Chenni, S. Semaoui, C. Z. El-Bayeh, and H. A. Hassan, βOptimal energy management system for
distribution systems using simultaneous integration of PV-based DG and DSTATCOM units,β Energetika, vol. 66, no. 1,
pp. 1-14, 2020, doi: 10.6001/energetika.v66i1.4294.
[11] M. B. Eteiba, S. Barakat, M. M. Samy, and W. I. Wahba, βOptimization of an off-grid PV/Biomass hybrid system with different
battery technologies,β Sustainable Cities and Society, vol. 40, pp. 713-727, 2018, doi: 10.1016/j.scs.2018.01.012.
[12] C. Mokhtara, B. Negrou, N. Settou, B. Settou, and M. M. Samy, βDesign optimization of off-grid hybrid renewable energy
systems considering the effects of building energy performance and climate change: Case study of Algeria,β Energy, vol. 219,
pp. 119605, 2021, doi: 10.1016/j.energy.2020.119605.
[13] M. M. Samy and S. Barakat, "Hybrid invasive weed optimization - particle swarm optimization algorithm for biomass/PV micro-
grid power system," 2019 21st International Middle East Power Systems Conference (MEPCON), 2019, pp. 377-382,
doi: 10.1109/MEPCON47431.2019.9008156.
[14] M. M. Samy, M. I. Mosaad, and S. Barakat, βOptimal economic study of hybrid PV-wind-fuel cell system integrated to unreliable
electric utility using hybrid search optimization technique,β International Journal of Hydrogen Energy, vol. 46, no. 20, pp. 11217-
11231, 2021, doi: 10.1016/j.ijhydene.2020.07.258.
[15] S. Ganesh and R. Kanimozhi, βMeta-heuristic technique for network reconfiguration in distribution system with photovoltaic and
D-STATCOM,β IET Generation, Transmission and Distribution, vol. 12, no. 20, pp. 4524-4535, 2018, doi: 10.1049/iet-
gtd.2018.5629.
[16] A. Bagherinasab, M. Zadehbagheri, S. A. Khalid, M. Gandomkar, and N. A. Azli, βOptimal placement of D-STATCOM using
hybrid genetic and ant colony algorithm to losses reduction,β International Journal of Applied Power Engineering (IJAPE),
vol. 2, no. 2, pp. 53-60, 2013, doi: 10.11591/ijape.v2i2.2408.
[17] T. Yuvaraj, K. R. Devabalaji, and S. B. Thanikanti, βSimultaneous allocation of DG and DSTATCOM using whale optimization
algorithm,β Iranian Journal of Science and Technology, Transactions of Electrical Engineering, vol. 44, no. 2, pp. 879-896, 2020,
doi: 10.1007/s40998-019-00272-w.
[18] K. R. Devabalaji and K. Ravi, βOptimal size and siting of multiple DG and DSTATCOM in radial distribution system using
bacterial foraging optimization algorithm,β Ain Shams Engineering Journal, vol. 7, no. 3, pp. 959-971, 2016,
doi: 10.1016/j.asej.2015.07.002.
[19] A. K. Arya, A. Kumar, and S. Chanana, βAssessment of deployment of DGs and D-STATCOMs in distribution network using
gravitational search algorithm,β International Journal of Recent Technology and Engineering (IJRTE), vol. 8, no. 5, pp. 119-127,
2020, doi: 10.35940/ijrte.d9009.018520.
[20] M. H. Moradi and M. Abedini, βA combination of genetic algorithm and particle swarm optimization for optimal DG location and
sizing in distribution systems,β International Journal of Electrical Power and Energy Systems, vol. 34, no. 1, pp. 66-74, 2012,
doi: 10.1016/j.ijepes.2011.08.023.
[21] S. F. Mekhamer, R. H. Shehata, A. Y. Abdelaziz, and M. A. Al-Gabalawy, βEnhancing radial distribution system performance by
optimal placement of DSTATCOM,β International Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 3,
pp. 2850-2860, 2020, doi: 10.11591/ijece.v10i3.pp2850-2860.
12. Int J Elec & Comp Eng ISSN: 2088-8708 ο²
A hybrid algorithm for voltage stability enhancement of β¦ (Hazim Sadeq Mohsin Al-Wazni)
61
[22] Y. Latreche, H. R. E. H. Bouchekara, M. S. Javaid, M. M. Aman, H. Mokhlis, and F. Kerrour, βOptimal incorporation of multiple
distributed generation units based on a new system maximum loadability computation approach and vortex searching algorithm,β
International Journal of Applied Power Engineering (IJAPE), vol. 8, no. 2, pp. 186-208, 2019, doi: 10.11591/ijape.v8.i2.pp186-
208.
[23] V. V. S. N. Murty and A. Kumar, βImpact of D-STATCOM in distribution systems with load growth on stability margin
enhancement and energy savings using PSO and GAMS,β International Transactions on Electrical Energy Systems, vol. 28,
no. 11, pp. 1-24, 2018, doi: 10.1002/etep.2624.
[24] S. R. Salkuti, βOptimal location and sizing of DG and D-STATCOM in distribution networks,β Indonesian Journal of Electrical
Engineering and Computer Science (IJEECS), vol. 16, no. 3, pp. 1107-1114, 2019, doi: 10.11591/ijeecs.v16.i3.pp1107-1114.
[25] A. Selim, S. Kamel, L. Nasrat, and F. Jurado, βVoltage stability assessment of radial distribution systems including optimal
allocation of distributed generators,β International Journal of Interactive Multimedia and Artificial Intelligence, vol. 6, no. 1,
pp. 32-40, 2020, doi: 10.9781/ijimai.2020.02.004.
[26] K. Rabyi and H. Mahmoudi, βEnergy storage of DFIG based wind farm using D-STATCOM,β International Journal of Electrical
and Computer Engineering (IJECE), vol. 9, no. 2, pp. 761-770, 2019, doi: 10.11591/ijece.v9i2.pp761-770.
[27] S. Devi and M. Geethanjali, βOptimal location and sizing determination of distributed generation and DSTATCOM using particle
swarm optimization algorithm,β International Journal of Electrical Power and Energy Systems, vol. 62, pp. 562-570, 2014,
doi: 10.1016/j.ijepes.2014.05.015.
[28] D. K. Rukmani et al., βA new approach to optimal location and sizing of DSTATCOM in radial distribution networks using bio-
inspired cuckoo search algorithm,β Energies, vol. 13, no. 18, 2020, doi: 10.3390/en13184615.
[29] O. Garfi, H. Aloui, and N. Chaker, βImpacts of photovoltaic power source intermittence on a distribution network,β International
Journal of Electrical and Computer Engineering (IJECE), vol. 9, no. 6, pp. 5134-5142, 2019, doi: 10.11591/ijece.v9i6.pp5134-
5142.
[30] S. Y. Reddy, D. S. Reddy, and G. K. Rao, βOptimal siting and sizing of solar power sources in interconnection grid system,β
International Journal of Applied Power Engineering (IJAPE), vol. 5, no. 1, pp. 1-13, 2016, doi: 10.11591/ijape.v5.i1.pp1-13.
[31] I. I. Ali and M. N. Mohsen, βEnhancement voltage stability of the Iraqi ower grid using shunt FACTs devices,β Engineering and
Technology Journal, vol. 34, no. 13, pp. 2527-2550, 2016.
[32] Δ°. B. Aydilek, βA hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems,β
Applied Soft Computing, vol. 66, pp. 232-249, 2018, doi: 10.1016/j.asoc.2018.02.025.
[33] A. Zeinalzadeh, A. Estebsari and A. Bahmanyar, "Simultaneous optimal placement and sizing of DSTATCOM and parallel
capacitors in distribution networks using multi-objective PSO," 2019 IEEE Milan PowerTech, 2019, pp. 1-6, doi:
10.1109/PTC.2019.8810577.
[34] M. M. Aman, G. B. Jasmon, A. H. A. Bakar, and H. Mokhlis, βA new approach for optimum DG placement and sizing based on
voltage stability maximization and minimization of power losses,β Energy Conversion and Management, vol. 70, pp. 202β210,
2013, doi: 10.1016/j.enconman.2013.02.015.
[35] L. F. Grisales-NoreΓ±a, D. G. Montoya, and C. A. Ramos-Paja, βOptimal sizing and location of distributed generators based on
PBIL and PSO techniques,β Energies, vol. 11, no. 4, pp. 1-27, 2018, doi: 10.3390/en11041018.
[36] M. Soliman, A. Y. Abdelaziz, and R. M. El-Hassani, βDistribution power system reconfiguration using whale optimization
algorithm,β International Journal of Applied Power Engineering (IJAPE), vol. 9, no. 1, pp. 48-57, 2020, doi:
10.11591/ijape.v9.i1.pp48-57.
[37] I. I. Ali and O. Y. Saeed, βOptimal reconfiguration and distributed generation placement in Baghdad distribution sector,β
Engineering and Technology Journal, vol. 36, no. 3, pp. 333-343, 2018, doi: 10.30684/etj.36.3a.13.
BIOGRAPHIES OF AUTHORS
Hazim Sadeq Mohsin Al-Wazni was born in 1981. He received his B.Sc. degree
in Electrical Engineering from University of Babylon, Iraq in 2003. Presently he is pursuing
M.Sc. In Electrical Power Engineering in Department of Electrical Engineering at Technology
University, Iraq. He has more than 16 years of experience in mantainus of electrical
distribution networks. His major scientific interest is focused on optimal location of DG and
D-STATCOM devices, modelling and simulation of distribution power system. He can be
contacted at email: hazimwazni83@gmail.com.
Shatha Suhbat Abdulla Al-Kubragyi received her B.Sc. and M.Sc degree in
Electrical and Electronic Engineering from University of Technology, Baghdad, Iraq, in 2000
and 2003, respectively. She was awarded a Ph.D. degree from University of Cranfield, UK in
2018. Since 2005, she has been a Lecturer in Electrical Engineering in the Department of
Engineering at the University of Technology. Her research interests includes power system
analysis, microgrids , renewable energy technologies, FACTS devices, and power system
operation and control. She can be contacted at email: Shatha.S.Abdulla@uotechnology.edu.iq.